Solve for $x$ and $y$ using elimination. ${4x-4y = 12}$ ${3x+5y = 33}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-3$ and the bottom equation by $4$ ${-12x+12y = -36}$ $12x+20y = 132$ Add the top and bottom equations together. $32y = 96$ $\dfrac{32y}{{32}} = \dfrac{96}{{32}}$ ${y = 3}$ Now that you know ${y = 3}$ , plug it back into $\thinspace {4x-4y = 12}\thinspace$ to find $x$ ${4x - 4}{(3)}{= 12}$ $4x-12 = 12$ $4x-12{+12} = 12{+12}$ $4x = 24$ $\dfrac{4x}{{4}} = \dfrac{24}{{4}}$ ${x = 6}$ You can also plug ${y = 3}$ into $\thinspace {3x+5y = 33}\thinspace$ and get the same answer for $x$ : ${3x + 5}{(3)}{= 33}$ ${x = 6}$